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A ray of light undergoes deviation of 30º when incident on an equilateral prism of refractive index √2. What is the angle subtended by the ray inside the prism with the base of the prism. 

(a) 30º

(b) 60º

(c) 90º

(d) zero 

1 Answer

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Best answer

Correct Option :- (d) zero 

Explanation :-

Here δ = 30º, A = 60º

so if the prism had been in a minimum deviation 

μ = sin {(A+δm)/2}/ sin (A/2) 

μ = sin {(60+30)/2}/ sin (60/2) 

μ = sin 45º/ sin 30º 

μ = (1/√2)*2 = √2 

Refractive index of prism is also given as √2, 

the prism is in the position of minimum deviation. 

This in turn implies that r1 = r2=r = A/2 = 60/2 = 30º 

So the angle subtended by the ray inside the prism with surface AB is equal to 

90-r1 = 90-30 = 60º 

As base also subtends an angle of 60º with the face AB. 

Hence the ray inside the prism is parallel to the base. 

i.e. the angle subtended by the ray inside the prism with the base is zero.

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